A276872 Sums-complement of the Beatty sequence for sqrt(6).

1, 6, 11, 16, 21, 28, 33, 38, 43, 50, 55, 60, 65, 70, 77, 82, 87, 92, 99, 104, 109, 114, 119, 126, 131, 136, 141, 148, 153, 158, 163, 168, 175, 180, 185, 190, 197, 202, 207, 212, 217, 224, 229, 234, 239, 246, 251, 256, 261, 268, 273, 278, 283, 288, 295, 300

Offset

1,2

Comments

See A276871 for a definition of sums-complement and guide to related sequences.

Links

Table of n, a(n) for n=1..56.

Index entries for sequences related to Beatty sequences

Example

The Beatty sequence for sqrt(6) is A022840 = (0, 2, 4, 7, 9, 12, 14, 17,...), with difference sequence s = A276856 = (2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 2,...).  The sums s(j)+s(j+1)+...+s(k) include (2,3,4,5,7,8,9,10,12,...), with complement (1,6,11,16,21,...).

Mathematica

z = 500; r = Sqrt[6]; b = Table[Floor[k*r], {k, 0, z}]; (* A022840 *)
t = Differences[b]; (* A276856 *)
c[k_, n_] := Sum[t[[i]], {i, n, n + k - 1}];
u[k_] := Union[Table[c[k, n], {n, 1, z - k + 1}]];
w = Flatten[Table[u[k], {k, 1, z}]]; Complement[Range[Max[w]], w];  (* A276872 *)

Crossrefs

Cf. A022840, A276856, A276871.

Sequence in context: A315478 A315479 A315480 * A376491 A315481 A315482

Adjacent sequences: A276869 A276870 A276871 * A276873 A276874 A276875

Keyword

nonn,easy

Author

Clark Kimberling, Sep 26 2016

Status

approved